Entry requirements

120 credits including 75 credits in physics and mathematics.

Learning outcomes

After successful completion of the course, the student is expected to be able to:

• represent time series with linear functions, polynomials or splines,
• analyse time series for deterministic or statistical behaviour,
• transform time series to spectra with Fourier transformation,
• understand the processes leading to aliasing and spectral leakage and design filters to prevent aliasing and leakage,
• compare the performance of different filters in time and frequency domain.

Content

Least-squares approximations: linear functions, polynomial functions, splines. Deterministic and statistical time series.

Fourier expansion: sampling theorem; finite record length, leakage and windowing. Practical estimation of spectra: discrete and Fast Fourier transform; convolution, covariance and correlation; covariance of power spectral estimates. Time and frequency filtering: convolution and deconvolution; shaping filters; spiking filters; matched filters; prediction filters. Z- transform, wavelets and applications as filters.

Instruction

Lectures, homework, problem solving and computer exercises.

Assessment

Take-home examination (3 credits) and homework assignments (2 credits).